TY - JOUR
N2 - In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo and Riemann-Liouvile equations and we also show an explicit formula for the solution of systems of time-invariant Caputo equations.
L1 - http://journals.pan.pl/Content/113668/PDF/08_749-760_01073_Bpast.No.67-4_30.08.19_K1_TeX.pdf
L2 - http://journals.pan.pl/Content/113668
PY - 2019
IS - No. 4
EP - 759
DO - 10.24425/bpasts.2019.130184
KW - linear discrete-time fractional systems
KW - Caputo equation
KW - Riemann-Liouville equation
KW - Volterra convolution equation
KW - stability
A1 - Anh, P.T.
A1 - Babiarz, A.
A1 - Czornik, A.
A1 - Niezabitowski, M.
A1 - Siegmund, S.
VL - 67
DA - 31.08.2019
T1 - Asymptotic properties of discrete linear fractional equations
SP - 749
UR - http://journals.pan.pl/dlibra/publication/edition/113668
T2 - Bulletin of the Polish Academy of Sciences: Technical Sciences
ER -